Reactor perfectly-stirred tank

CONTINUOUS FLOW ISOTHERMAL PERFECTLY STIRRED TANK REACTOR... 

LCB affects the properties of LDPE, low density polyethylene made by free-radical polymerization see Section 10. The continuous polymerization is carried out in stirred reactors or in tubes several authors (5, 90, 92) have considered the effects of LCB on MWD in perfectly-stirred tank reactors. 

An ideal batch reactor is a perfectly stirred tank of constant volume with no mass transfer from or to the outside. There is a single residence time, which is simply the duration of the reaction. Generally, a batch reactor is operated isothermally and therefore the reaction temperature may be considered as an independent variable. 

Many of these difficulties can be overcome by choosing an appropriate configuration of the photoreactor system. One such a system is the mechanically agitated cylindrical reactor with parabolic reflector. In this type of reactor, the reaction system is isolated from the radiation source (which could also simplify the solution of the well-known problem of wall deposits, generally more severe at the radiation entrance wall). The reactor system uses a cylindrical reactor irradiated from the bottom by a tubular source located at the focal axis of a cylindrical reflector of parabolic cross-section (Fig. 40). Since the cylindrical reactor may be a perfectly stirred tank reactor, this device is especially required. This type of reactor is applicable for both laboratory-and commercial-scale work and can be used in batch, semibatch, or continuous operations. Problems of corrosion and sealing can be easily handled in this system. 

Consider the steady operation of a perfectly-stirred tank reactor (CSTR) of constant volume V, in which only homogeneous reactions occur. Again, the system for the b2dances is chosen as the fluid contents of the reactor. Eq. (3.1-4) then gives... 

A well-stirred reactor containing solid catalysts can be modelled as a perfect stirred tank reactor, that is, concentration is the same everywhere inside the reactor. When such catalysts are very small, the diffusional resistance inside the catalyst can be ignored. The catalyst is slowly... 

In order to describe adequately the hydrodynamics of the experimental fixed bed reactor, it is necessary to take into account the axial dispersion in the mathematical model. The time dependent continuity equation including axial dispersion for a fixed bed reactor is given by a partial differential equation (pde) of the parabolic/hyperbolic class. These types of pde s are difficult to solve numerically, resulting in long cpu times. A way to overcome these difficulties is by describing the fixed bed reactor as a cascade of perfectly stirred tank reactors. The axial dispersion is then accounted for by the number of tanks in series. For a low degree of dispersion (Bo < 50) the number of stirred tanks, N, and the Bodenstein number. Bo, are related as N Bo/2 [8].The fixed bed reactor is now described by a system of ordinary differential equations (ode s). No radial gradients are taken into account and a onedimensional model is applied. Mass balances are developed for both the gas phase and the adsorbed phase. The reactor is considered to be isothermal. 

Figure 15.5 Two-reactor model of imperfect mixing in a CSTR. (a) Idealized CSTR in which mixing is perfect and concentrations are homogeneous throughout the reactor, (b) Stirred tank with cross flow between active (well-mixed) and dead (poorly mixed) zones. Q represents volume flow, C is concentration, k is flow rate (reciprocal residence time), and V is volume. Subscripts i specifies chemical species, 0 signifies input from reservoirs, r is homogeneous reactor, and a and d are active and dead zones, respectively. (Adapted from Kumpinsky and Epstein, 1985.)...

Figure 12.1. Modeling mixing by associating a Lagrangian model, which calculates the movements ofEFPs, with a model calculating their mixing in a fluid volume regarded as a perfectly stirred tank reactor...

Figure 12.2. Implementation process of mixing models in a perfectly stirred tank reactor. The fluid volume is fragmented into EFPs of the size of the Kolmogorov scale...

The name continuous flow-stirred tank reactor is nicely descriptive of a type of reactor that frequently for both production and fundamental kinetic studies. Unfortunately, this name, abbreviated as CSTR, misses the essence of the idealization completely. The ideality arises from the assumption in the analysis that the reactor is perfectly mixed, and that it is homogeneous. A better name for this model might be continuous perfectly mixed reactor (CPMR). 

If the mixing is "perfect," tlie estuary behavior may be approximated by what chemical engineers define as a continuous stirred tank reactor (CSTR) (5). However, accurately estimating the time and spatial beliavior of water quality in estuaries is complicated by the effects of tidal motion as just described. The upstream and downstream currents produce substantial variations of water quality at certain points in the estuary, and tlie calculation of such variation is indeed a complicated problem. How ei er, the following simplifications provide some reiiitirkably useful results in estimating the distribution of estuarine water quality. 

Mixing Models. The assumption of perfect or micro-mixing is frequently made for continuous stirred tank reactors and the ensuing reactor model used for design and optimization studies. For well-agitated reactors with moderate reaction rates and for reaction media which are not too viscous, this model is often justified. Micro-mixed reactors are characterized by uniform concentrations throughout the reactor and an exponential residence time distribution function. 

The perfectly mixed, continuous-how stirred tank reactor (CSTR)... 

Chapter 2 treated multiple and complex reactions in an ideal batch reactor. The reactor was ideal in the sense that mixing was assumed to be instantaneous and complete throughout the vessel. Real batch reactors will approximate ideal behavior when the characteristic time for mixing is short compared with the reaction half-life. Industrial batch reactors have inlet and outlet ports and an agitation system. The same hardware can be converted to continuous operation. To do this, just feed and discharge continuously. If the reactor is well mixed in the batch mode, it is likely to remain so in the continuous mode, as least for the same reaction. The assumption of instantaneous and perfect mixing remains a reasonable approximation, but the batch reactor has become a continuous-flow stirred tank. 

Perfectly mixed stirred tank reactors have no spatial variations in composition or physical properties within the reactor or in the exit from it. Everything inside the system is uniform except at the very entrance. Molecules experience a step change in environment immediately upon entering. A perfectly mixed CSTR has only two environments one at the inlet and one inside the reactor and at the outlet. These environments are specifled by a set of compositions and operating conditions that have only two values either bi ,..., Ti or Uout, bout, , Pout, Tout- When the reactor is at a steady state, the inlet and outlet properties are related by algebraic equations. The piston flow reactors and real flow reactors show a more gradual change from inlet to outlet, and the inlet and outlet properties are related by differential equations. 

A real continuous-flow stirred tank will approximate a perfectly mixed CSTR provided that tmix h/i and tmix i. Mixing time correlations are developed using batch vessels, but they can be applied to flow vessels provided the ratio of throughput to circulatory flow is small. This idea is explored in Section 4.5.3 where a recycle loop reactor is used as a model of an internally agitated vessel. 

Stirred tanks are often used for gas-liquid reactions. The usual geometry is for the liquid to enter at the top of the reactor and to leave at the bottom. The gas enters through a sparge ring underneath the impeller and leaves through the vapor space at the top of the reactor. A simple but effective way of modeling this and many similar situations is to assume perfect mixing within each phase. 

Copolymerizations. The uniform chemical environment of a CSTR makes it ideally suited for the production of copolymers. If the assumption of perfect mixing is justified, there will be no macroscopic composition distribution due to monomer drift, but the mixing time must remain short upon scaleup. See Sections 1.5 and 4.4. A real stirred tank or loop reactor will more closely... 

Reactor design usually begins in the laboratory with a kinetic study. Data are taken in small-scale, specially designed equipment that hopefully (but not inevitably) approximates an ideal, isothermal reactor batch, perfectly mixed stirred tank, or piston flow. The laboratory data are fit to a kinetic model using the methods of Chapter 7. The kinetic model is then combined with a transport model to give the overall design. 

We have just described a completely segregated stirred tank reactor. It is one of the ideal flow reactors discussed in Section 1.4. It has an exponential distribution of residence times but a reaction environment that is very different from that within a perfectly mixed stirred tank. 

The difference between complete segregation and maximum mixedness is largest when the reactor is a stirred tank and is zero when the reactor is a PFR. Even for the stirred tank case, it has been difficult to find experimental evidence of segregation for single-phase reactions. Real CSTRs approximate perfect mixing when observed on the time and distance scales appropriate to industrial reactions, provided that the feed is premixed. Even with unmixed... 

The principle of the perfectly-mixed stirred tank has been discussed previously in Sec. 1.2.2, and this provides essential building block for modelling applications. In this section, the concept is applied to tank type reactor systems and stagewise mass transfer applications, such that the resulting model equations often appear in the form of linked sets of first-order difference differential equations. Solution by digital simulation works well for small problems, in which the number of equations are relatively small and where the problem is not compounded by stiffness or by the need for iterative procedures. For these reasons, the dynamic modelling of the continuous distillation columns in this section is intended only as a demonstration of method, rather than as a realistic attempt at solution. For the solution of complex distillation problems, the reader is referred to commercial dynamic simulation packages. 

In the second model (Figure 5.1b), the mixed-flow or continuous well-mixed or continuous-stirred-tank (CSTR) model, feed and product takeoff are both continuous, and the reactor contents are assumed to be perfectly mixed. This leads to uniform composition and temperature throughout the reactor. Because of the perfect mixing, a fluid element can leave the instant it enters the reactor or stay for an extended period. The residence time of individual fluid elements in the reactor varies. 

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